It is given that in a triangle ABC, a line from A to BC intersects BC at point D. If the ratio in which AD divides BC is given can we say anything about the ratio of areas of triangle ABD and triangle ADC ?

1 Answer
1

Yes we can find the ratio of the areas of the two triangles.
Area of $\triangle ADC$=$$(AD\times DC\times\sin\theta)\over2$$
Area of $\triangle ABD$=$$(AD\times DB\times \sin(180^\circ-\theta))\over2$$
[$\theta$ is the angle $ADC$]

Divide these two equations and use the ratio you have to get the answer.